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\( x^{2}+9x+8 = (x+1)(x+8) \)
Solución
Factor the expression \( x^{2}+9x+8 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}+9x+8\)
- step1: Rewrite the expression:
\(x^{2}+\left(8+1\right)x+8\)
- step2: Calculate:
\(x^{2}+8x+x+8\)
- step3: Rewrite the expression:
\(x\times x+x\times 8+x+8\)
- step4: Factor the expression:
\(x\left(x+8\right)+x+8\)
- step5: Factor the expression:
\(\left(x+1\right)\left(x+8\right)\)
The fully factored form of \(x^{2}+9x+8\) is \((x+1)(x+8)\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To fully factorise the quadratic expression \( x^{2}+9x+8 \), we look for two numbers that multiply to 8 (the constant term) and add up to 9 (the coefficient of the linear term). The numbers 8 and 1 fit this criteria since \( 8 \times 1 = 8 \) and \( 8 + 1 = 9 \). Thus, we can write the expression as: \[ x^{2} + 9x + 8 = (x + 8)(x + 1) \] This is the fully factorised form of the given quadratic expression.
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